5. Cable BAC is used to lift the normally distributed load lb. If the system is in the position shown below, determine the probability that the system may fail. The allowable tension of the cable AB follows another normally distribution N. Assume that T and W are independently distributed.

Solution

Then, we have

Therefore, we have

Thus, the probability of failure of the system is that , where .

Also, we have

Finally, the probability of failure is

Ans.